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6390, , Conventions for working out expressions BODMAS, © MathSphere, , Page 2, , www.mathsphere.co.uk, , For the next two pages you need 2 types of calculator - an ordinary one, and a scientific calculator., It is very important that when you are faced with a series of sums in a, line that they are calculated in the correct order. Believe it or not this, may not be the order that they come! Look below:, Work out the answer to 3 + 5 x 5 =, Is there a possibility of more than one correct answer?, Try a scientific calculator and see what answer you get., , Try an ordinary calculator and see what answer you get., Can you write why you think the, calculators come up with two different, answers?, , Huh! Who said, calculators gave you, the right answer!, , To get the answer 40 the addition is done first, followed by the, multiplication., To get the answer 28 the multiplication is done first followed by the, addition., Which is correct?, Good question!, Try these sums on the two different calculators:, 1. 3 + 3 x 4 =, , or, , 2. 20 – 6 x 2 =, , or, , 3. 6 x 6 + 4 =, , or, , 4. 48 – 12 ÷ 4 =, , or, , Can you see what the scientific calculator is doing?

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , www.mathsphere.co.uk, , Page 3, , If a long sum (or expression) has no brackets, like 3 + 5 x 5 = it, has been agreed by mathematicians that the multiplying would be, worked out before the addition, even if it does not appear first in, the sum., If a sum has a bracket as part of it, such as 4 x (5 + 4) = then it has, been agreed that the part inside the brackets will be calculated, first., There is an easy way to remember this: BODMAS, , Brackets, Of, Division, Multiplication, Addition, Subtraction, , Any sum in brackets is, calculated first., Division and multiplication are, calculated before addition and, subtraction., , Try these to get the idea!, 1., , 6+ 4 x2 =, , 2., , 4+ 4÷2 =, , 3., , 8 + 6–3 =, , 4., , 5+5 x 4 =, , 5., , 12 + 3 x 2 =, , 6., , 2 x 4+5 =, , Not as hard as I thought!, I can have a break now!

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , www.mathsphere.co.uk, , Page 4, , Remember BODMAS. Any calculations inside brackets, must be completed before any other part of the sequence., Without using a calculator work out the answers to the, following sequences:, 1. 100 – (20 x 3) =, , 9., , 2. (35 – 15) + (27 – 7) =, , 10., , 56 – (4 x 7) =, , 3. 15 + (6 x 6) =, , 11., , 78 – (10 x 7) =, , 4. (4 + 5) x (3 + 6) =, , 12., , (7 x 7) + (4 x 8) =, , 5. (5 + 5) x (5 – 2) =, , 13. (45 – 23) + (5 x 8) =, , 6. 50 – (6 x 6) =, , 14., , 38 – (5 x 7) =, , 7. (4 + 8) x (3 – 2) =, , 15., , (100 – 45) + (7 x 7) =, , 8. (9 – 3) + (6 x 6) =, , 16., , 45 – (9 x 4) =, , Not so tricky eh! I bet, you got all these, correct!, , (5 x 7) – (2 x 5) =, , Just a couple of trickier, problems., By putting in brackets in, different places, how many, different sums and answers, can you find for these two, sequences:, 1., , 4+4x5–3=, , 2., , 8+5x1+3–6=

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , www.mathsphere.co.uk, , Page 5, , Remember BODMAS shows you the order in which, operations should be carried out., What is the value of ;, 1. (4 x 2 ) + ( 3 x 3 ) =, , 2. ( 4 x 4 ) + ( 5 x 5 ) =, , 3. ( 6 x 6 ) – ( 4 x 4 ) =, , 4. ( 9 x 9 ) – ( 8 x 8 ) =, , 5. 18 – ( 4 x 2 ) =, , 6. 4 x ( 4 – 2 ) =, , 7. 18 – ( 9 x 4 ) + 32 =, , 8. ( 12 x 12 ) – ( 11 x 12 ) =, , 9. 30 – ( 5 x 4 ) =, , 10. 67 – ( 9 x 5 ) =, , 11. ( 8 + 6 ) x 4 =, , 12. 8 x 7 – 3 =, , 13. (4 x 9) – ( 4 x 8 ) =, , 14. 56 – ( 5 x 9 ) =, , 15. 72 – (8 x 7 ) + 9 =, , 16. (9 x 8) + ( 9 x 8 ) =, , Wow! I bet you got most of, these right as well., Getting easy aren't they!, Try finding a sequence, that will give the same, answer if you put the, brackets in two different, places.

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , Page 6, , www.mathsphere.co.uk, , Remember BODMAS shows you the order in which operations, should be carried out., Write the following sums out without changing the order of the, numbers. To make the sums correct put in the brackets if, necessary to show which part has to be completed first., , 8+4 x 6 – 5, , =, , 27, , 8+4 x 6 – 5, , =, , 12, , 8+4 x 6 – 5, , =, , 67, , You can see the need for a rule on this otherwise, everyone would be doing sums in different ways and, getting different answers!, Put in the signs and/or brackets to make the following true:, , 1., , 4, , 4, , 3, , = 16, , 6., , 4, , 6, , 4, , =, , 20, , 2., , 7, , 6, , 11, , = 12, , 7., , 10, , 3, , 5, , =, , 35, , 3., , 2, , 2, , 4, , =, , 8, , 8., , 2, , 4, , 6, , =, , 1, , 4., , 2, , 2, , 4, , = 16, , 9., , 24, , 2, , 4, , =, , 8, , 5., , 4, , 3, , 3, , =, , 10., , 5, , 4, , 4, , =, , 21, , 13, , Ah ha! I bet you, didn't find these, quite as easy!, You did? Great!

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , www.mathsphere.co.uk, , Do you remember what these signs mean?, , < means is less than, > means is more than, , Page 7, , < and >, , The arrow, always, points to the, smaller, number!, , Put the correct sign into the statements below. You will have, to work out the sums first, remembering BODMAS, , 1., , 6+4x3, , 3x4+6, , 2., , 8 x 8 – 20, , 6 x 6 + 20, , 3. 2 x 32 + 46, , 62 + 4 x 9, , 4., , 6+8x8, , 8+8x6, , 5. 120 – 6 x 7, , 6 x 7 + 40, , 6. 140 + 4 x 7, , 32 x 5 + 5, , Investigate: Using only these numbers and signs make a, statement or expression which will give you the biggest, possible answer:, , 8 + 7 – 6, , x 4 and one set of brackets.

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , www.mathsphere.co.uk, , Page 8, , SPEED CHECK: USING THE CORRECT SEQUENCE OF, OPERATIONS, Time yourself on these questions to see how long it takes., Remember to work out the answer in the right order (BODMAS), , 1. 9 x (4 + 4) =, , 2. 8 x (3 + 8) =, , 3. 5 x (6+ 3) =, , 4. 8 + 24 ÷ 4 =, , 5. 7 + 63 ÷ 9 =, , 6. 5 + 21 ÷ 7 =, , 7. (4 + 7) x 3 =, , 8., , 9. (7 + 2) x 8 =, , 10., , 11., , 12 ÷ (2 + 4) =, , ( 5 + 3) x 6 =, 24 ÷ (7 + 5) =, , 12. 45 ÷ (4 + 5) =, , 13. 63 ÷ (17 – 8) =, , 14. 4 + 5 x 9 =, , 15. 8 + 8 x 8 =, , 16., , 7+7x7=, , 17. 6 + 6 x 6 =, , 18. 9 + 9 x 9 =, , 19., , 81 – 4 x 4 =, , 20. (18 + 15) – (13 + 12) =, , How long did you take?, Did you get them all correct?

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , Page 9, , www.mathsphere.co.uk, , SPEED CHECK: USING THE CORRECT SEQUENCE OF, OPERATIONS, Time yourself on these questions to see how long it takes., , Remember to work out the answer in the right order, (BODMAS)., 1. 8 x (5 + 4) =, , 2. 7 x (4 + 8) =, , 3. 6 x (6+ 4) =, , 4. 7 + 28 ÷ 4 =, , 5. 6 + 72 ÷ 9 =, , 6. 4 + 28 ÷ 7 =, , 7. (3 + 8) x 5 =, , 8. (6 + 4) x 8 =, , 9. (9 + 2) x 7 =, , 10. 32 ÷ (4 + 4) =, , 11. 18 ÷ (7 + 2) =, , 12. 54 ÷ (4 + 5) =, , 13. 48 ÷ (14 – 8) =, Even speedier!!, , 14. 5 + 5 x 8 =, , 15. 6 + 7 x 8 =, , 16., , 8+9x6=, , 17. 4 + 6 x 7 =, , 18. 3 + 4 x 5 =, , 19., , 64 – 4 x 4 =, , 20. (19 + 13) – (14 + 15) =, , How long did you take? If this was your second go, did you, beat your first time?, Did you get them all correct?

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6390, , Conventions for working out expressions BODMAS, © MathSphere, , Page 10, , www.mathsphere.co.uk, , ANSWERS, Page 2, 1. 24 or 15, Page 3, 1.14, , 2. 28 or 8, , 2. 6, , 3. 40 or 40, , 3. 11, , 4. 25, , 4., , 9 or 45, , 5. 18, , 6. 13, , Page 4, 1. 40, 2. 40, 9. 25 10. 28, , 3. 51, 11. 8, , 4. 81, 12. 81, , 5. 30, 13. 62, , 6. 14, 14. 3, , 7. 12, 15. 104, , 8. 42, 16. 9, , Page 5, 1. 17, 2. 41, 9. 10 10. 22, , 3. 20, 11. 56, , 4. 17, 12. 53, , 5. 10, 13. 4, , 6. 8, 14. 11, , 7. 14, 15. 25, , 8. 12, 16. 144, , Page 6, , 8 + (4 x 6) – 5 = 27, , (8 + 4) x (6 – 5) = 12, , 1. 4 + (4 x 3) = 16, 2. (7 – 6) + 11 = 12, 3. 2 + 2 + 4 = 8 or 2 x 2 + 4 = 8, 4. (2 + 2) x 4 = 16, 5. 4 + (3 x 3) = 13, Page 7, 1. 18 = 18 2. 44 < 56, Page 8, 1. 72 2. 88, 11. 2, , 12. 5, , Page 9, 1. 72 2. 84, 11. 2, , 12. 6, , 3. 45, 13. 7, , 3. 60, 13. 8, , (8 + 4) x 6 – 5 = 67, , 6. 4 x 6 – 4 = 20 or (4 x 6) – 4 = 20, 7. (10 – 3) x 5 = 35 or 10 x 3 + 5 = 35, 8. (2 + 4) ÷ 6 = 1, 9. 24 ÷ 2 – 4 = 8 or (24 ÷ 2) – 4 = 8, 10. 5 + (4 x 4) = 21, , 3. 110 > 98, , 4. 56 < 70, , 5. 78 < 82, , 6. 168 > 165, , 4. 14, , 5. 14, , 6. 8, , 7. 33, , 8. 48, , 9. 72, , 10. 2, , 14. 49, , 15. 72, , 16. 56, , 17. 42, , 18. 90, , 19. 65, , 20. 8, , 4. 14, , 5. 14, , 6. 8, , 7. 55, , 8. 80, , 9. 77, , 10. 4, , 14. 45, , 15. 62, , 16. 62, , 17. 46, , 18. 23, , 19. 48, , 20. 3